ApCoCoA-1:BB.GenHomMultMat

This article is about a function from ApCoCoA-1.

BB.GenHomMultMat

Computes a generic homogeneous multiplication matrix.

Syntax

BB.GenHomMultMat(I:INT,OO:LIST):MAT

Description

Computes the generic homogeneous multiplication matrix for x[I] with respect to an order ideal. The inputs are an integer I and a list OO of terms that specify an order ideal. The second element of OO must be a non-constant polynomial. The output is a matrix of size Len(OO) x Len(OO) over the ring BBS=K[c_{ij}].

• @param I An integer which specifies the indeterminate for which the generic homogeneous multiplication matrix will be computed.

• @param OO A list of terms representing an order ideal.

• @return The generic homogeneous multiplication matrix.

Example

Use QQ[x, y, z], DegRevLex;
BB.GenHomMultMat(1, [1, x, x^2, y, z]);

-------------------------------
Mat([
  [0, 0, 0, 0, 0],
  [1, 0, 0, 0, 0],
  [0, 1, 0, BBS :: c[3,5], BBS :: c[3,3]],
  [0, 0, 0, 0, 0],
  [0, 0, 0, 0, 0]
])
-------------------------------